How do I apply a fill (color)?

I know this is a really stupid question for those of you who know what you're doing - but I don't. Example: I start a new file, draw a box with the rectangle tool, or some other shape with the pen tool, select the shape with the select tool or direct select tool, open the color picker, pick a color, click OK - and nothing happens. I then go to "Edit", and Fill (and stroke) are both greyed-out. What am I missing? And the gradient tool... I tried using it on a simple shape with a solid color, and the instant the cursor touches anywhere on the artboard, it turns into the "No" symbol (slashed circle) and when I click it says "Could not use the gradient tool because the content of the layer is not directly editable". Any help would be greatly appreciated. Thank you.